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please solve soon and completely with following parameters for numerical 5) (5 pts) u(x,t) is solution...
u(x,t) is solution to heat equation, ,with following parameters for numerical approximation: 0 < x < 2, 0 < t < 0.1, n = 20, m = 100, c =1. Boundary conditions: u(0,t) =0, and u(2,0) = 0. Initial conditions: u (x,0) =30o for 0<x<=1 0o for 1<x<2 Set the approximate difference equation for this equation. Do you think this equation converges to a numerical solution. Continuing with problem 1, calculate u(0.1,0.001) by iteration Continuing with problem 1, calculate u(0.2,0.001)...
Let u be the solution to the initial boundary value problem for the Heat Equation, dụı(t, x)-20 11(t, x), IE(0, oo), XE(0,3); with initial condition u(0,x)-f (x), where f(0) 0 andf'(3)0, and with boundary conditions Using separation of variables, the solution of this problem is with the normalization conditions 3 a. (5/10) Find the functions wn, with index n 1. wn(x) = 1 . b. (5/10) Find the functions vn, with index n Let u be the solution to the...
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t, x)-5 &n(t, x), t E (0,00), x E (0, 1); with initial condition 2 r-, 1 and with boundary condition:s n(t, 0)=0, rn(t, 1-0. Find the solution u using the expansion with the normalization conditions vn (0)-1, wn a. (3/10) Find the functions wz, with indexn> 1 b. (3/10) Find the functions v, with index n> 1. c. (4/10) Find the coefficients cn, with...
Let u be the solution to the initial boundary value problem for the Heat Equation au(t,) -48Fu(t,), te (0,oo), z (0,5); with boundary conditions u(t,0) 0, u(t,5) 0, and with initial condition 5 15 15 The solution u of the problem above, with the conventions given in class, has the form with the normalization conditions vn(0)-1, u Find the functions vnwn and the constants cn n(t) wnr) Let u be the solution to the initial boundary value problem for the...
Let u be the solution to the initial boundary value problem for the Heat Equation дли(t, 2) — 4 әғи(t, 2), te (0, o0), те (0,1); with initial condition , u(0, a)f() and with boundary conditions 0. u(t, 0)0 u(t, 1) Find the solution u using the expansion и(t, г) "(2)"т (?)"а " n 1 with the normalization conditions 1 Vn (0) 1, wn 2n a. (3/10) Find the functions wn, with index n> 1. Wn b. (3/10) Find the...
Can you do this on MATLAB please? Thanks. (1) [20 pts] Find the exact solution to the Initial Boundary- Value problem utV x E (0,1), t>0, a(0, t)=0, a(i, t) = 0, t>0, t 20. Write the scheme and a code (forward in time, center in space) to approximate the solution of this prob- lem for u = 1/6. Take ΔⅡ 0.1 and compare your results with the exact solution at t = 0.01, 0.1, 1, 10 with At0.01 (1)...
Please show all work and provide and an original solution. We can apply the Method of Separation of Variables to obtain a representation for the solution u u(, t) for the following partial differential equation (PDE) on a bounded domain with homogeneous boundary conditions. The PDE model is given by: u(r, 0) 0, (2,0) = 4. u(0,t)0, t 0 t 0 (a) (20 points) Assume that the solution to this PDE model has the form u(x,t) -X (r) T(t). State...
Let u be the solution to the initial boundary value problem for the Heat Equation u(t, x) 4ut, x) te (0, o0), т€ (0, 3)%; with initial condition 2. f(x) u(0, x) 3 0. and with boundary conditions ди(t, 0) — 0, и(t, 3) — 0. Find the solution u using the expansion u(t, a) "(2)"п (?)"а " п-1 with the normalization conditions Vn (0) 1, wn(0) = 1 a. (3/10) Find the functions wn. with index n > 1....
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z 382u(t,z), tE (0,oo), E (0,3); with initial condition u(0,x)-f(x)- and with boundary conditions Find the solution u using the expansion u(t,x) n (t) wn(x), with the normalization conditions vn (0)1, Wn (2n -1) a. (3/10) Find the functionswn with index n 1. b. (3/10) Find the functions vn, with index n 1 C. (4/10) Find the coefficients cn , with index n 1. Let...
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1, t> 0 u(x, 0, 1) = 0, uy(x,1,1) = 0, with boundary conditions u(O, y,t) = 0, u(r, y, t) = 0, and initial condition u(x, y,0) = (y – į v?) sin(2x).